We study the nonreciprocal excitation and entanglement dynamics of two giant atoms (GAs) coupling to a one-dimensional waveguide. With different positions of coupling points, three configurations of two separate GAs, two braided GAs, and two nested GAs are analyzed, respectively. The coupling strengths between different coupling points are considered as complex numbers with phases. For each coupling configuration, the nonreciprocal excitation dynamics and entanglement properties, which results from the phase differences of coupling strength and the phase induced by photon propagation between the two coupling points, are studied both in Markovian and non-Markovian regimes. The analytical solutions for nonreciprocal entanglement degree are given in the Markovian regime. It shows that the steady entanglement can be reached and strongly depends on the phases. Different from the case of the Markovian regime, the entanglement degree shows oscillating behavior in the non-Markovian regime. This work may find applications in the generation and controlling of entanglement in quantum networks based on waveguide quantum electrodynamics.